f(5) = 3 means (5,3) is on the graph of f.
On the new graph, y = f(x+1) + 2, what do the +1 and +2 do?
Things inside the function notation inpact the x-values, since that's where x sits.
This outside the f(x) notation impact the y-values, since those are done after you've evaluated the function.
"+1" on the inside shifts every point to the left 1 unit. (Inside changes are almost always opposite from what it looks like it would do.)
"+2" on the outside will shift every point up by 2 units.
So what do you get if you take (5,3) and shift it left 1 and up 2?
Answer:
see below
Step-by-step explanation:
Part A: (72)^x = 1
Take the log base 72 of each side
log72(72^x) = log 72(1)
We know log a^b = b log a
x log72(72) = log72(1)
x = log72(1)
x = 0
Part A: (70)^x = 1
Take the log base 70 of each side
log70(70^x) = log70(1)
We know log a^b = b log a
x log70(70) = log70(1)
x = log70(1)
x = 0
This can solved using the cosine law which is:
c² = a² + b² - 2ab cos θ
Using the values given from the problem
6² = b² + b² - 2bb cos 112.62
And solving for b
36 = 2b² - 2b² cos 112.62
b = 3.6
The answer is the 3rd option.
